ORGANISATION/COMPANYUniversité Clermont Auvergne
RESEARCH FIELDComputer scienceMathematics
RESEARCHER PROFILEFirst Stage Researcher (R1)
APPLICATION DEADLINE28/06/2020 00:00 - Europe/Brussels
LOCATIONFrance › AUBIERE
TYPE OF CONTRACTTemporary
HOURS PER WEEK35 H
OFFER STARTING DATE01/10/2020
IS THE JOB RELATED TO STAFF POSITION WITHIN A RESEARCH INFRASTRUCTURE?Yes
Subject: Towards a mathematical understanding of neural networks through
Supervisor: Arnaud Guillin
Laboratory: Laboratoire Mathématiques Blaise Pascal
Email and phone: email@example.com, 0473407090
Co-advisor(s): Manon Michel (LMBP)
Abstract (up to 10 lines):
If deep neural networks have proved their efficiency in a number of real
applications (game of Go, image analysis,…), we are far from understanding
the mathematical reasons behind this success. Recently a mean field analysis
has been introduced to get a new perspective on these algorithms. We will
pursue this direction and make links with statistical physics to hopefully gain a
profund understanding of these new statistical learning tools.
Skills: Mathematics, Probability, Statistics, Statistical learning, R,
Keywords: Deep neural networks, statistical learning, mean field
Description (up to 1 page):
The recent developments of Machine Learning algorithms have been marked
by popular successes, in particular coming from neural networks and their deep
implementation. However such successes are still poorly rigorously justified
and the rich behavior of deep neural nets is yet to be characterized by a wellunderstood
mathematical framework. In this thesis, we propose to work
towards such formalism by use of a mean field analysis. First developed for spin
systems and then applied in the 80s to shallow neural nets by physicists, the
mean field approach is the object of a recent renewed interest in mathematics
for such problems, thanks to its simplification power. However, this
simplification comes with limitations which need to be precisely analysed.
Eventually, the mean-field approach allows to draw natural bridges with
statistical physics, namely the spin-glass community, which will be also
"Mean field analysis of neural networks: A central limit theorem", Konstantinos Spiliopoulos,
Justin Sirignano, Stochastic Processes and their Applications , Volume 130, Issue 3, March
2020, pp. 1820-1852.
Deep Neural Networks Motivated by Partial Differential Equations, Lars Ruthotto, Eldad
Haber. Arxiv 2019.
"Mean field analysis of neural networks: a law of large numbers", Konstantinos Siliopoulos,
Justin Sirignano, 2019, SIAM Journal on Applied Mathematics, to appear.
Explorations on high dimensional landscapes, G. Ben Arous, L. Sagun, V. Ugur Guney, and
Yann Le Cun International Conference on learning representations, ICLR 2015
Références (up to ½ page):
How to candidate?
Contact the supervisor
REQUIRED EDUCATION LEVELOther: Master Degree or equivalent
EURAXESS offer ID: 528445
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